b. ~(x)(Fx~Gx) = (3x)(Fx Gx) (~E= 1)

Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Chapter1: Line And Angle Relationships
Section1.4: Relationships: Perpendicular Lines
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Problem b

3. Using just Q.N. and your propositional replacement rules, derive the following C.Q.N.
equivalences.
*a. ~(3x)(Fx*~Gx) = (x)(FxGx)
b. ~(x) (Fx ~Gx) = (3x)(Fx Gx)
*c. (3x)(Fx Gx) = (x)(Fx~Gx)
(~0 = A)
(~E= 1)
(~1 = E)
Transcribed Image Text:3. Using just Q.N. and your propositional replacement rules, derive the following C.Q.N. equivalences. *a. ~(3x)(Fx*~Gx) = (x)(FxGx) b. ~(x) (Fx ~Gx) = (3x)(Fx Gx) *c. (3x)(Fx Gx) = (x)(Fx~Gx) (~0 = A) (~E= 1) (~1 = E)
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